Correction of non-uniform sensitivity in an image array

ABSTRACT

An improved non-uniform sensitivity correction algorithm for use in an imager device (e.g., a CMOS APS). The algorithm provides zones having flexible boundaries which can be reconfigured depending upon the type of lens being used in a given application. Each pixel within each zone is multiplied by a correction factor dependent upon the particular zone while the pixel is being read out from the array. The amount of sensitivity adjustment required for a given pixel depends on the type of lens being used, and the same correction unit can be used with multiple lenses where the zone boundaries and the correction factors are adjusted for each lens. In addition, the algorithm makes adjustments to the zone boundaries based upon a misalignment between the centers of the lens being used and the APS array.

This application is a continuation of application Ser. No. 10/915,454,filed Aug. 11, 2004, now U.S. Pat. No. 7,609,302, the disclosure ofwhich is incorporated herein by reference in its entirety.

FIELD OF THE INVENTION

The present invention relates generally to complementary metal oxidesemiconductor (CMOS) imagers, and more particularly to correction ofnon-uniform sensitivity in pixels of such imagers.

BACKGROUND OF THE INVENTION

A CMOS image sensor is an imaging device built with CMOS technology forcapturing and processing light signals. Results produced by the CMOSimage sensor can be displayed. A type of CMOS image sensors, called aCMOS Active Pixel Sensors (APS), has been shown to be particularlysuited for handheld imaging applications.

The CMOS APS comprises an array of pixel processing elements, each ofwhich processes a corresponding pixel of a received image. Each of thepixel processing elements includes a photo-detector element (e.g., aphotodiode or a photogate) for detecting brightness information in thereceived image, and active transistors (e.g., an amplifier) for readingout and amplifying the light signals in the received image. Theamplification of the light signals allows circuitry in the CMOS APS tofunction correctly with even a small amount of the received lightsignals.

The CMOS APS also has color processing capabilities. The array of pixelprocessing elements employs a color filter array (CFA) to separate red,green, and blue information from a received color image. Specifically,each of the pixel processing elements is covered with a red, a green, ora blue filter, according to a specific pattern, e.g., the “Bayer” CFApattern. As a result of the filtering, each pixel of the color imagecaptured by a CMOS APS with CFA only contains one of the three colors.

For example, while a given pixel may have data on how much red wasreceived by that pixel, it does not have any data as to how much blue orgreen was received by that pixel. The “missing” values are recovered bya technique called interpolation whereby the values of each color forthe surrounding pixels are averaged in order to estimate how much ofthat color was received by the given pixel.

While CMOS APSs have been well-received by industry and consumers alike,there are still some shortcomings. For example, as described above, eachpixel contains a number of different parts required for capturing theimage. The different parts are not ideal, of course, and can producesensitivity variations over the array. With reference to FIG. 1, a CMOSAPS contains a pixel array implemented in Si 100. The CMOS APS alsocontains a layer of protective Si oxide 105 which may also serve as asupport for metal interconnects. The CMOS APS array further includes acolor filter array 110 (e.g., a Bayer CFA) to allow only light of aspecific wavelength to pass to each pixel within the active pixel area100. The FIG. 1 CMOS APS also contains a layer of microlenses 115 thatconcentrates the incident light in the sensitive area of the underlyingpixel and a main lens 120 that focuses the light rays 125 from theobject onto the microlenses 115.

Most of the components described above, due to imperfections orpractical limitations, may contribute to spatial signal attenuation,which in turn results in a sensitivity variation over the array.Further, it is known that for a given lens, the pixels of the APS havevarying degrees of sensitivity depending upon their geographic locationon the array. The rule of thumb is that the further away from the centerof the APS the more correction the pixel requires. This phenomenon canadversely effect the images produced by the APS.

Often these variations can be measured and corrected as they mostlydepend on the lens design used and generally do not vary from part topart. Such correction can be done in post-processing of already-acquiredimage data or during image acquisition (i.e., as the image is read outfrom the APS).

Since pixel sensitivity depends in part on the geometric location of agiven pixel, generally speaking, one “global” correction function is notsatisfactory. Prior knowledge of the non-uniform sensitivity of thepixels, when used with a particular type of lens, is used to generate aplurality of correction functions that are applied to (e.g., multipliedby) the pixel values as they are read out. In order to increase thespecial precision of the correction functions, the array is divided intoa number of “zones,” where each zone includes a predetermined number ofpixels and where the pixels of each zone are multiplied by a correctionfactor depending upon the zone and the pixel location relative to theAPS center.

For example, a 640×640 pixel array may include 4 zones in thex-direction and 4 zones in the y-direction where each zone contains 128rows or columns of pixels. Another example is to divide the APS arrayinto a number of zones where the zones are configured to optimize aparticular lens that is used. The boundaries of the zones, however,cannot be modified to accommodate any other lenses that may be used.

One disadvantage of the prior art is that the zones of known correctionalgorithms are fixed by design. That is, while a given non-uniformsensitivity correction algorithm may work well for a given type of lens,the algorithm does not work as well with another type of lens. Anotherdisadvantage associated with the prior art is that when the center ofthe lens is not perfectly aligned with the center of the APS array, asis often the case, there is currently no method to take that offset intoaccount and to adjust the zone boundaries for it.

BRIEF SUMMARY OF THE INVENTION

The present invention addresses the shortcoming described above andprovides an improved non-uniform sensitivity correction algorithm foruse in an imager device (e.g., a CMOS APS). The algorithm provides forzones having flexible boundaries which can be reconfigured dependingupon the type of lens being used in a given application. Each pixelwithin each zone is multiplied by a correction factor dependent upon theparticular zone and pixel position while the pixel is being read outfrom the array. The amount of sensitivity adjustment required for agiven pixel depends on the type of lens being used, and the samecorrection unit can be used with multiple lenses where the zoneboundaries and the correction factors are adjusted for each lens. Inaddition, the algorithm makes adjustments to the zone boundaries basedupon any misalignment between the centers of the lens being used and theAPS array.

BRIEF DESCRIPTION OF THE DRAWINGS

The above and other features and advantages of the invention will bemore readily understood from the following detailed description of theinvention which is provided in connection with the accompanyingdrawings, in which:

FIG. 1 depicts a schematic cross-sectional view of a conventional CMOSimage sensor array;

FIG. 2 depicts an APS array divided into zones, in accordance with anexemplary embodiment of the invention;

FIG. 3 depicts the FIG. 2 APS array coupled to readout circuitry andoptionally on an imager integrated circuit chip;

FIG. 4 depicts a flow chart describing an operation flow of thesensitivity correction algorithm, in accordance with an exemplaryembodiment of the invention;

FIG. 5 depicts a flow chart describing an operational flow forgenerating a sensitivity correction algorithm, in accordance with anexemplary embodiment of the invention;

FIG. 6 depicts a flow chart describing a more detailed operational flowfor generating a sensitivity correction algorithm, in accordance with anexemplary embodiment of the invention; and

FIG. 7 depicts a processor based system containing the FIG. 3 APS array,in accordance with an exemplary embodiment of the invention.

DETAILED DESCRIPTION OF THE INVENTION

In the following detailed description, reference is made to theaccompanying drawings which form a part hereof, and in which is shown byway of illustration specific embodiments in which the invention may bepracticed. These embodiments are described in sufficient detail toenable those of ordinary skill in the art to make and use the invention,and it is to be understood that structural, logical or proceduralchanges may be made to the specific embodiments disclosed withoutdeparting from the spirit and scope of the present invention.

FIG. 2 depicts an APS array divided into several zones, in accordancewith an exemplary embodiment of the invention. The zones depicted inFIG. 2 represent the optimum geographic location of the zones when theAPS array is used in conjunction with a certain type of lens. Theboundaries of the zones are programmable and may be modified to anotherconfiguration so that the APS array may be used with another type oflens. As depicted, the array is divided into eight different zones inthe x-direction (defined by X₀ through X₇) and eight different zones inthe y-direction (defined by Y₀ through Y₇). The coordinates of zoneboundaries are referenced respectively to the center point of the lens(lens principle axis). The coordinates Cx and Cy are, in turn, specifiedwith respect to the center of the APS array. As depicted in FIG. 2, thecoordinates Cx and Cy represent the center of the lens correctionfunctions in both the x-direction and the y-direction. When the centersof the lens and the APS array are aligned, the values of Cx and Cy arezero. However, when the center of the APS array is not aligned with thecenter of the lens, as is often the case, in accordance with thisexemplary embodiment of the invention, that misalignment is identified,quantified and taken into account with respect to the zone boundaries.

The corrected pixel signal, P(x, y), is equal to the readout pixelvalue, P_(IN)(x, y), multiplied by the correction function, F(x, y). Theembodiment of the correction function is represented by the followingexpression:F(x,y)=θ(x, x ²)+φ(y, y ²)+k*θ(x, x ²)*φ(y, y ²)+G   (1)where θ(x, x²) represents a piecewise parabolic correction function inthe x-direction, where φ(y, y²) represents a piecewise paraboliccorrection function in the y-direction, where k*θ(x, x²)*φ(y, y²) isused to increase the lens correction values in the array corners, andwhere G represents a “global” gain (increase or decrease) applied toevery pixel in the array, regardless of pixel location and zone.

Further, within each zone, the functions θ(x, x²) and φ(y, y²) arerespectively represented by the generic expressions:a_(i)x²+b_(i)x+c_(i), and a_(i)y²+b_(i)y+c_(i) where i is the zonenumber.

In order to generate functions θ(x, x²) and φ(y, y²), as used in Eq. 1,initial conditions for each of these functions are specified. Functionsθ and φ are generated for each color (red, green, or blue) separately toallow for color-specific correction. The initial conditions include aset of initial values of the correction functions and their “firstderivatives.” These initial conditions are stored in memory (e.g.,registers). This is done once for the entire array and is not requiredto be done for each zone. Initial conditions are specified for eachcolor where only two colors are required for each line in the case of aBayer pattern.

The “first derivative” of the correction function for each pixel is thenet increase or decrease in the correction function value as comparedwith its adjacent pixel. The first derivatives are stored in memory(e.g., a register) and generally changed with each step. For each nextpixel of the same color adjacent to (e.g., to the right of) the secondpixel, the net increase or decrease from the second pixel correctionvalue (i.e., the first derivative of the third pixel) is stored in aregister. In addition, the difference between the first derivative ofthe second pixel and the first derivative of the third pixel is storedin a register. The difference between the first derivative of the secondpixel and the first derivative of the third pixel is called the “secondderivative” of the correction function for that pixel and is also storedin a register. A set of color-specific second derivative values isstored for each zone. Functions θ and φ are then produced iteratively(using the value obtained on the previous step) using zone-specifiedvalues for the second derivatives.

For example, with reference to FIG. 2, assume the initial value of atop-left-most red pixel in zone 1 is 100 and the desired correctionfunction value for the next red pixel to the right of the first redpixel is 104. Also assume that the correction function value of thethird red pixel immediately to the right of the second red pixel is 110.These values are known in advance since the user already knows the typeof lens being used with the array and already knows the optimum zoneboundaries and correction functiHHon values to be applied to each pixeland for each color. The first derivative of the second red pixel is 4since that is the net difference between the correction function valueof the first and second red pixels. The first derivative of the thirdred pixel is 6 since that is the net difference between the correctionfunction values of the second and third red pixels. In addition, thesecond derivative of the third pixel is 2 since that is the differencebetween the respective first derivatives of the second and third redpixels.

In accordance with an exemplary embodiment of the invention, the initialvalues of the two correction function and their first derivatives arestored in registers as well as second derivatives for each zone. Thesecond derivative is a constant for a given zone (i.e., for all pixelsin a given zone). The second derivatives are specified for all zonesthroughout the set of registers. As each pixel is read out from thearray, the correction function value corresponding to that pixel iscalculated and multiplied by the pixel value, resulting in the correctedpixel value, P(x, y). Storing the first and second derivatives of thepixels in each zone rather than each and every correction function valuerequires far less memory capacity.

Although the initial values are demonstrated as being assigned to thetop left-most pixel, the initial value can be assigned to any pixel inthe zone (e.g., the bottom right-most pixel, etc.) or to more than onepixel in the zone. In such a case, the pixels may be read out in twodifferent directions. In accordance with an exemplary embodiment of theinvention, the correction values may be introduced into the pixelsignals as they are being read out in either normal mode, in mirroringmode (i.e., when the direction in which the pixels are read out isreversed), or in a dual-direction readout mode. The initial values areassigned for θ(x, x²) at the beginning of each line while initialconditions for φ(y, y²) are assigned only once at the first line of theframe.

Also, in accordance with an exemplary embodiment of the invention, thesecond derivative within a given zone does not change. Therefore, thedifference between the first derivatives of pixels in a zone is the samewithin a given zone. Accordingly, zones are pre-selected so that therequired correction function could be represented accurate enough byonly one set of second derivatives for this zone. The pixels within thezone require approximately the same degree of sensitivity correction.

Further, in accordance with an exemplary embodiment of the invention, inorder to assure a smooth transition from one zone to an adjacent zone,the functions θ(x, x²) and φ(y, y²), as well as their first derivatives,are equal at the point of transition from zone to zone. This produces apiecewise quadratic polynomial expression known as a quadratic spline.

It should be noted that under dark conditions, the effects of thecorrection algorithm should be minimized to avoid noise amplification.The pixel signal being read out has two components; a signal componentproportional to the amount of light registered in the pixel and a noisecomponent, which at very low light levels is represented in large extentby a pixel temporal noise. Thus, if one were to apply the correctionfunction to the array in the dark condition, the temporal noise of thepixel array would also be changed. In practice, this would result in thenoise component increasing towards the sides of the image array. Toavoid this artifact, in accordance with an exemplary embodiment of theinvention, the degree to which the correction algorithm is applied tothe pixel signals depends upon the magnitude of the pixel illumination.This could be effectuated by adjusting the G value in Eq. 1 based on theexposure value for the current scene. That is, in dark conditions, whenthe degree of lens correction is lessened, the G parameter is increased.As a result, the share of the x, y components in the function F(x, y),and thus noise amplification, is significantly reduced.

Moreover, during preview mode, where the resolution is not as high as innormal mode, the correction algorithm is still employed. Rather thanreading out every pixel in the array and multiplying each pixel by thecorresponding correction value, fewer than every pixel (e.g., everyother pixel) is read out and multiplied by its corresponding sensitivitycorrection value. In this manner, even during preview mode, the pixelsof the array that are read out have relatively uniform sensitivity.

With reference to FIG. 3, as the pixel values are read from the APSarray 305, they are transferred to processing circuitry via column bus300. In accordance with an exemplary embodiment of the invention, thepixel values are passed through a sensitivity correction unit 315 whichmultiplies the respective pixel values, as they are read out from thearray 305, by a correction function value. This process compensates forthe inherent differences in sensitivity for the pixels and generates atruer image. Memory 310 (e.g., a register, etc.) stores the initialvalues of the pixels in each zone and also stores the first and secondderivatives of the respective pixels in the zones. As a result, thememory 310 need not store every correction function value of everypixel, but only the “roadmap” of how to get to those values. Thereafter,the corrected pixel signals are forwarded to sample/hold circuit 320,analog-to-digital converter 325, pixel processor 330 and output circuit335, per the usual practice.

FIG. 3 also depicts the pixel sensor array 350 as being integrated ontoor within an integrated circuit (IC) chip 380. The chip 380 may be madeof any material suitable for use with pixel sensor arrays, includingsilicon-based materials, glass-based materials, etc.

FIG. 4 depicts a flowchart illustrating an operational flow of thesensitivity correction algorithm, in accordance with an exemplaryembodiment of the invention. The operation begins at segment 400 and atsegment 405, a determination is made at the sensitivity correction unitas to which lens type, of the plurality of lens types capable of beingused with the sensitivity correction unit, it being used in theapplication. At segment 410, the zone boundaries of the pixel array andsensitivity correction values for the pixels are selected depending onwhich lens type has been selected. At segment 412, a determination ismade as to whether the respective centers of the pixel array 305 and alens being used with the pixel array are misaligned. If yes, then thedegree of misalignment is determined and an adjustment to the zoneboundaries is made at segment 414. If they are not misaligned or whenthe adjustment has been made for the misalignment, then the processproceeds to segment 415.

At segment 415, the pixels of the pixel array 305 are read out whilebeing multiplied by their respectively assigned correction values.Further processing of the pixel signals is performed at segment 420 andthe process ends at segment 425.

FIG. 5 depicts a flowchart demonstrating an operational flow of thegeneration of the sensitivity correction algorithm, in accordance withan exemplary embodiment of the invention. The process begins at segment500 and at segment 505, a determination is made as to which lens typesare being used for the application. At segment 510, for a selected lenstype, a plurality of zones are identified into which the pixels of thepixel array 305 are divided. In accordance with an exemplary embodimentof the invention, the boundaries of the zones, as well as the number ofzones, are programmable based on the type of lens being used.

At segment 515, initial sensitivity correction values and firstderivatives of at least one pixel in a first zone in each of the x and ydirections are stored in memory 310 (e.g., a register). At segment 520,second derivative values are generated and stored for each pixel in eachzone of the pixel array 310. At segment 520, a determination is made asto whether there is another lens type to add to the algorithm. If yes,then the process returns to segment 510. If not, then the process endsat segment 530.

FIG. 6 depicts a flow chart describing a more detailed operational flowfor generating a sensitivity correction algorithm, in accordance with anexemplary embodiment of the invention. The process begins at segment 600and at segment 605, initial correction values are stored for each zone.At segment 610, the correction value of the next pixel in the zone isidentified (this is predetermined based on the type of lens being used).At segment 615, the difference between the initial correction value andthe correction value of the next pixel is determined. At segment 620,the first derivative of the next pixel is stored.

At segment 625, the correction value of the next pixel in the zone isidentified. At segment 630, the difference between the correction valueof the next pixel in the zone and the previous pixel in the zone isdetermined. At segment 640, the first derivative of the pixel at segment625 is stored. At segment 645, the difference between the firstderivatives stored at segments 620 and 640 is determined and at segment650, the second derivative of the pixel at segment 625 is stored.

Still referring to FIG. 6, at segment 655, a determination is made as towhether there are any other pixels in the zone. If yes, then the processreturns to segment 625 and repeats segments 625 through 655. If no otherpixels in the zone, then the process ends at segment 665.

FIG. 7 shows system 700, a typical processor based system modified toinclude an image sensor IC as in FIG. 3. Processor based systemsexemplify systems of digital circuits that could include an imagesensor. Examples of processor based systems include, without limitation,computer systems, camera systems, scanners, machine vision systems,vehicle navigation systems, video telephones, surveillance systems, autofocus systems, star tracker systems, motion detection systems, imagestabilization systems, and data compression systems for high-definitiontelevision, any of which could utilize the invention.

System 700 includes central processing unit (CPU) 702 that communicateswith various devices over bus 704. Some of the devices connected to bus704 provide communication into and out of system 700, illustrativelyincluding input/output (I/O) device 706 and image sensor IC 408. Otherdevices connected to bus 704 provide memory, illustratively includingrandom access memory (RAM) 710, hard drive 712, and one or moreperipheral memory devices such as floppy disk drive 714 and compact disk(CD) drive 716.

Image sensor 708 can be implemented as an integrated image sensorcircuit on a chip 380 with a non-uniform sensitivity correction unit315, as illustrated in FIG. 3. Image sensor 708 may be combined with aprocessor, such as a CPU, digital signal processor, or microprocessor,in a single integrated circuit.

As described above, the disclosed algorithm provides zones havingflexible boundaries which can be reconfigured depending upon the type oflens being used in a given application. The disclosed algorithm alsoprovides for a simplified application method in which initial values ofcorrection functions are stored and when pixel signals are read out fromthe array, the correction functions are easily applied to those signalswhile minimizing required storage. In addition, the algorithm makesadjustments to the zone boundaries based upon any misalignment betweenthe center of the lens being used and the center of the APS array.Further, adjustments to the degree with which the correction algorithmis applied depending upon the quantity of light the pixel is exposed tois also disclosed. Exemplary embodiments of the present invention havebeen described in connection with the figures.

While the invention has been described in detail in connection withpreferred embodiments known at the time, it should be readily understoodthat the invention is not limited to the disclosed embodiments. Rather,the invention can be modified to incorporate any number of variations,alterations, substitutions or equivalent arrangements not heretoforedescribed, but which are commensurate with the spirit and scope of theinvention. For example, while the invention is described in connectionwith a CMOS pixel imager, it can be practiced with any other type ofpixel imager (e.g., CCD, etc.). In addition, although the invention isdescribed in connection with eight programmable zones in each of thex-direction and the y-direction, the invention can be practiced with anynumber of programmable zones. Accordingly, the invention is not limitedby the foregoing description or drawings, but is only limited by thescope of the appended claims.

1. An imager device, comprising: a pixel array comprising a plurality ofmicrolens and a plurality of pixels, wherein the pixel array capturesimages focused onto the pixel array by a main lens; and a sensitivitycorrection unit coupled to the pixel array, wherein the sensitivitycorrection unit selectively corrects the sensitivity of pixel signalsfrom the plurality of pixels according to a correction function assignedto each pixel, and wherein the sensitivity correction unit determineswhether the main lens and the pixel array are misaligned and reassignsthe correction functions to the pixels to compensate for a misalignment.2. The imager device of claim 1, wherein the sensitivity correction unitdivides the pixels into an arrangement of zones, each zone including aplurality of pixels, and corrects the sensitivity of pixel signals frompixels within the zones, and wherein the sensitivity correction unitadjusts the arrangement of the zones to compensate for a misalignment.3. The imager device of claim 1 further comprising: a sample and holdcircuit coupled to the sensitivity correction unit for receivingcorrected pixel signals; an analog-to-digital converter coupled to thesample and hold circuit for converting sampled corrected pixel signalsto digital format; and a pixel processor for processing the digitalcorrected pixel signals.
 4. The imager device of claim 1, furthercomprising a memory device storing at least one correction functionassigned to one pixel.
 5. The imager device of claim 4, wherein thememory device stores a plurality of derivatives of the correctionfunctions assigned to the pixels.
 6. The imager device of claim 1,wherein the sensitivity correction unit assigns a first set ofcorrection functions to the pixels when a first main lens is used withthe imager device, and wherein the sensitivity correction unit assigns asecond and different set of correction functions to the pixels when asecond main lens is used with the imager device.
 7. The imager device ofclaim 1, wherein the sensitivity correction unit divides the pixels intoa first arrangement of zones when a first main lens is used with theimager device, and wherein the sensitivity correction unit divides thepixels into a second and different arrangement of zones when a secondmain lens is used with the imager device.
 8. The imager device of claim1, wherein the sensitivity correction unit adjusts the correctionfunction assigned to each pixel according to an amount of light receivedby the pixel array.
 9. A method of correcting sensitivity of pixels ofan imager device, the method comprising: determining whether a main lensis misaligned with a pixel array comprising a plurality of microlensesand a plurality of pixels; focusing light onto the pixel array throughthe main lens and producing a plurality of pixel signals from theplurality of pixels; and correcting the plurality of pixel signals byapplying a correction function to each pixel signal according to acorrection function scheme using a sensitivity correction unit; whereinthe sensitivity correction unit adjusts the correction function schemeaccording to a detected misalignment between the pixel array and themain lens.
 10. The method of claim 9, wherein the sensitivity correctionfunction scheme comprises a plurality of zones, each zone comprising aplurality of pixels.
 11. The method of claim 10, wherein the sensitivitycorrection unit changes which pixels are included in the zones to adjustthe correction function scheme according to the detected misalignmentbetween the pixel array and the main lens.
 12. The method of claim 9,further comprising: determining which main lens of a plurality of mainlenses is being used with the pixel array; applying a correctionfunction to the pixel signals according to a first correction functionscheme when a first main lens is being used with the pixel array; andapplying a correction function to the pixel signals according to asecond correction function scheme when a second main lens is being usedwith the pixel array.
 13. The method of claim 9 further comprising:forwarding at least one corrected pixel signal for at least one of thepixels to a sample and hold circuit; converting an output of the sampleand hold circuit to digital format; and conducting further pixelprocessing of a digital version of the at least one corrected pixelsignal.
 14. The method of claim 9, further comprising calculating thecorrection functions to be applied to the pixel signals usingderivatives of the correction functions of the correction functionscheme.
 15. An imager device, comprising: a pixel array comprising aplurality of microlens and a plurality of pixels, wherein the pixelarray captures images focused onto the pixel array by a main lens; asensitivity correction unit coupled to the pixel array, wherein thesensitivity correction unit selectively corrects the sensitivity ofpixel signals from the plurality of pixels according to a plurality ofcorrection functions; and a memory storing a plurality of derivatives ofthe correction functions, the plurality of derivatives comprising afirst derivative of the correction functions for less than all of theplurality of pixels, wherein a first derivative of the correctionfunctions is defined as the difference between two correction functions.16. The imager device of claim 15, wherein the memory further stores acorrection function for less than all of the plurality of pixels. 17.The imager device of claim 15, wherein the memory stores a plurality ofsecond derivatives of the correction functions, wherein a secondderivative of the correction functions is defined as the differencebetween two first derivatives of the correction functions, and wherein afirst derivative of the correction functions is defined as thedifference between two correction functions.
 18. The imager device ofclaim 17, wherein the sensitivity correction unit divides the pixelsinto zones, and wherein the zones comprise pixels having a common secondderivative of the correction functions.
 19. The imager device of claim18, wherein the memory stores a correction function and a firstderivative of a correction function for only one pixel from each zone.20. The imager device of claim 18, wherein the sensitivity correctionunit divides the pixels into a first arrangement of zones when a firstmain lens is used with the imager device, and wherein the sensitivitycorrection unit divides the pixels into a second and differentarrangement of zones when a second main lens is used with the imagerdevice.
 21. The imager device of claim 17, wherein the sensitivitycorrection unit calculates the correction functions for the plurality ofpixels using the plurality of second derivatives.
 22. The imager deviceof claim 17, wherein the first derivative of the correction functions isfurther defined as the difference between two correction functions forpixels of the same color, and wherein the second derivative of thecorrection functions is further defined as the difference between twofirst derivatives of the correction functions of pixels of the samecolor.
 23. A method of correcting sensitivity of pixels of an imagerdevice, the method comprising: projecting an image onto a pixel arraycomprising a plurality of pixels; producing a plurality of pixel signalsfrom the plurality of pixels; calculating a plurality of correctionfunctions using a plurality of derivatives of the correction functions;and correcting the plurality of pixel signals by applying the pluralityof correction functions to the plurality of pixel signals, the pluralityof derivatives comprising a first derivative of the correction functionsfor less than all of the plurality of pixels, wherein a first derivativeof the correction functions is defined as the difference between twocorrection functions.
 24. The method of claim 23, wherein the pluralityof derivatives comprise a plurality of second derivatives of thecorrection functions, wherein a second derivative of the correctionfunctions is defined as the difference between two first derivatives ofthe correction functions, and wherein a first derivative of thecorrection functions is defined as the difference between two correctionfunctions.
 25. The method of claim 24, further comprising dividing thepixels into a plurality of zones in which the pixels of each zone have acommon second derivative of the correction functions.
 26. The method ofclaim 25, further comprising calculating the correction functions forthe pixel of a zone using the common second derivative of the correctionfunctions, a first derivative of the correction functions for one of thepixels within the zone, and a correction function for one of the pixelswithin the zone.
 27. The method of claim 24, wherein the firstderivative of the correction functions is further defined as thedifference between two correction functions for pixels of the samecolor, and wherein the second derivative of the correction functions isfurther defined as the difference between two first derivatives of thecorrection functions of pixels of the same color.
 28. The method ofclaim 23, further comprising calculating the plurality of correctionfunctions using a first plurality of derivatives of a first plurality ofcorrection functions when a first main lens is used to project the imageonto the pixel array, and calculating the plurality of correctionfunctions using a second plurality of derivatives of a second pluralityof correction functions when a second main lens is used to project theimage onto the pixel array.